Monday, August 8, 2022

Texas Instruments: TI-36X Pro and TI-30X Pro Mathprint

 Essentially, the Texas Instruments TI-36X Pro and the TI-30X MathPrint are functionally equivalent.  What makes the two calculators different?


*  The TI-36X Pro is sold in the United States and in lot of the world, with the TI-30X MathPrint is sold primarily from Europe.  I ordered my TI-30X Pro MathPrint from the United Kingdom.  


Product pages from Texas Instruments:


TI-36X Pro (United States and Canada)

https://education.ti.com/en/products/calculators/scientific-calculators/ti-36x-pro


TI-30X MathPrint (Denmark, in Danish):

https://education.ti.com/da/products/calculators/scientific-calculators/ti-30x-pro-mp#specifications


Australia has a TI-30XPlus MathPrint, which is styled like the TI-30X Pro MathPrint, but without calculus functions.

https://education.ti.com/en-au/products/calculators/scientific-calculators/ti-30x-plus-mp?category=overview


*  Thanks to the body of the calculator being curved, the TI-36X Pro is slightly bigger than the TI-30X Pro MathPrint. 


*  The screen on the TI-36X Pro is a curved trapezoid, while the screen of the TI-30X Pro MathPrint has is rectangular.  


*  The TI-36X Pro has a circular arrow keypad while the TI-30X Pro MathPrint has a rectangular arrow keypad.  


* The TI-30X Pro Math print has black characters, while the TI-36X Pro has blue characters.


* The font on the keys of the TI-30X Pro Math are larger than than the font on the TI-36X Pro's keys.


Here are some pictures.













Either calculator is worth buying.  You  can see my review of the TI-36X Pro from 2011 here:

P.S. I still wish the TI-36X Pro/TI-30X Pro MathPrint had an alpha key instead of one key to press multiple times to get different variables.  That is my biggest gripe. 

Eddie



All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 






Sunday, August 7, 2022

Retro Review: Retro Review Radio Shack EC-480

Retro Review:   Retro Review Radio Shack EC-480








Quick Facts


Model:  EC-480

Company:  Radio Shack

Years:  1976-1977

Type:  Scientific 

Batteries: 2 x AA, separate AC power 

Operating Modes:  Chain

Number of Registers: 1

Display:  8 digits, 1 left character for shift and error indicator


The EC-480 comes to have a brown, thin faux-leather cover.  


Pocket Sized Scientific Calculator


The EC-480 is a no-frills, lightweight, scientific calculator: just the basics.   Most likely, this would be an on today's smartphones.  The keys are plastic and thankfully the keys are responsive.   You can hear a click when the keys are pressed.  


Every of the 20 keys has a shifted function.  A smart move is the put the ON-OFF switch instead of making it a key.  


The keyboard:


C/CE; 1/X

F; cf  (Shift; Clear Shift)

EEX; conv

÷; arc  (for arcsin, arccos, arctan)

7; sin

8; cos

9; tan

×; sto 

4; e^x

5; 10^x

6; y^x

-; rcl

1; ln

2; log

3; √

+; m+

+/-; x^2

0; π

.;  (

=; )


The angle measurement used is degrees.


The conv function toggles the screen.  When a number is big or small enough to show a exponent, the conv functions shows the mantissa.  For example:


5.5.638 E 11 

× 1.2365 E 10 

= 6.8796 E 21

(conv) 6.8796387   (6.8796387 * 10^21)

(conv) 6.8796 E 21


The one thing I do not like about the EC-480 is that sometimes the 10^x function is sometimes inaccurate due to rounding error.  For example:


10^3 returns 1000

10^4 returns 10000

10^5 returns 99999.999

10^6 returns 999999.99

10^7 returns 10000000


Try 2^x * 5^x instead.  (Possible keystrokes:  2 y^x x = sto 5 y^x x * rcl =)


No Order of Operations


The EC-480 does not follow the order of operations, instead of the chain operating system.  This may be a turn off for some people.  Just to illustrate this:


4 + 5 × 6 returns 54

4 + ( 5 × 6 ) returns 34

5 × 6 + 4 returns 34


Green Display


The display has 9 characters.  The right 8 contain numbers, with the left as an indicator.   


#.#.#.#.#.#.#.#.#.


The first decimal point indicator appears when you press the blue shift key.  


The left character is a negative sign with nothing else is when the calculator is sleeping.  I like this feature to save battery.  


Source


Flow Simulation Ltd.  "Radio Shack EC-480"  calculator.org 2022.  https://www.calculator.org/calculators/Radio_Shack_EC-480.html   Retrieved June 5, 2022


Eddie


All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


Saturday, August 6, 2022

HP 12C: Cash Back vs Credit Card Interest

HP 12C: Cash Back vs Credit Card Interest


Introduction


If you have a credit card, chances are that you have a cash back program, where the company offers you cash back rate based on qualified purchases.  Is the benefit worth it?  



HP 12C Program:  Cash Back vs. Interest


Store the following data:


PV:  current credit card balance

PMT:  qualified purchases

i% using [ g ] (12÷):  monthly credit card rate

R0 using [ STO ] 0:  cash back rate


This program assumes all purchases made qualify for the cash back rate.


Step #;  Step Key;  Key


01; 45, 14; RCL PMT

02; 45, 0;  RCL 0

03; 25; %

04; 31; R/S

05; 45, 13; RCL PV

06; 45, 14; RCL PMT

07; 40;  +

08; 45, 12; RCL i

09; 25; %

10; 31; R/S

11; 40; +

12; 43,33,00; GTO 00   (use GTO 000 on HP 12C Platinum)


Outputs:


1.  Cash back 

2.  Interest charged on the balance and purchases

3.  New balance


Examples


Example 1:


Credit card balance:  $1,000.00   

Qualified purchases:  $230.00

Credit card annual rate:  15%

Cash back rate:  5%


1000 [ PV ]

230 [ PMT ]

15 [ g ] (12÷)

5 [ STO ] 0


[ R/S ]:

11.50  [ R/S ]

15.38  [ R/S ]

1241.50


Cash back:  $11.50

Interest:  $15.38

New balance:  $1,241.50


Example 2:


Credit card balance:  $585.65   

Qualified purchases:  $176.19

Credit card annual rate:  16.79%

Cash back rate:  5%


585.65 [ PV ]

176.19 [ PMT ]

16.79 [ g ] (12÷)

5 [ STO ] 0


[ R/S ]:

8.81 [ R/S ]

10.66  [ R/S ]

772.50


Cash back:  $8.81

Interest:  $10.66

New balance:  $772.50


Investigation:  Cash Back Benefit vs. Credit Card Interest


I then wondered, is there a point where the cash back gives a better benefit than the interest charged.


Consider the equation:


cash back benefits = monthly interest charge

purchases * cash_back% = (balance + purchases) * monthly_interest%

purchases * (cash_back% - monthly_interest%) = balance * monthly_interest%

purchases * (cash_back% ÷ monthly_interest% - 1) = balance 

cash_back% ÷ monthly_interest% - 1 = balance ÷ purchases


Let the test ratio be defined as:


test ratio = cash_back% ÷ monthly_interest% - 1 


Using the data from Example 2:


test ratio = 5 ÷ (16.79 ÷ 12) - 1 ≈ 5 ÷ 1.40 - 1 ≈ 3.57 - 1 = 2.57


For the cash back and interest to be equal, the purchases must equal balance÷2.57 or $227.88.  Running the program, the cash back and interest charged is around $11.38.  


This means we will have to make a lot of qualified purchases.  Say if we spent $400.00 in purchases, the cash back is $20.00, with interest $13.79, and the balance $999.44.  


To try to do this on a continuous basis poses several problems:  we still have to pay the balance otherwise we have to buy more each month to get the greater benefit.  Also, the lower the starting balance, the lower the minimum purchase requirement.


With a credit card rate of 16.79% (monthly about 1.40%) and cash back 5%, the test ratio is (5 ÷ 1.4 - 1) is 2.57.  


A beginning balance of $200.00 will require $77.82 of qualified purchases (200 ÷ 2.57), while a beginning balance of $500.00 will require $194.55 in purchases.


Take care and have a great day,


Eddie


All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


Friday, August 5, 2022

Python - Lambda Week: Solving Differential Equations with Runge Kutta 4th Order Method

Python - Lambda Week: Solving Differential Equations with Runge Kutta 4th Order Method


Welcome to Python Week!  This we we're going to cover calculus and the keyword lambda.



Note:  All Python scripts presented this week were created using a TI-NSpire CX II CAS.   As of June 2022, the lambda keyword is available on all calculators (in the United States) that have Python.   If you are not sure, please check your calculator manual. 


Solving Differential Equations


This following script solves the differential equation:


y' = dy/dx = f(x,y)

with initial condition y(x0) = y0


Repeat the steps for each step size h:

f1 = h * f(x0, y0)

f2 = h * f(x0 + h/2, y0 + f1/2)

f3 = h * f(x0 + h/2, y0 + f2/2)

f4 = h * f(x0 + h, y0 + f3)

x0 = x0 + h   (update x)

y0 = y0 + (f1 + 2*f2 + 2*f3 + f4)/6   (update y)


The small h is, the more accurate the calculated coordinates are.  


rk4lam.py:  Runge Kutta 4th Order Method


All answers are stored in the nested list t.  


from math import *

print("Runge Kutta 4th Order")

print("Math Module imported")

f=eval("lambda x,y:"+input("dy/dx = "))


# must call for float numbers one at a time

x0=eval(input("x0 = "))

y0=eval(input("y0 = "))

h=eval(input("h = "))


# ask for an integer

n=int(input("number of steps: "))


# set up table

t=[[x0,y0]]


# main loop

for i in range(n):

  f1=h*f(x0,y0)

  f2=h*f(x0+h/2,y0+f1/2)

  f3=h*f(x0+h/2,y0+f2/2)

  f4=h*f(x0+h,y0+f3)

  x0=x0+h

  y0=y0+(f1+2*f2+2*f3+f4)/6

  print([x0,y0])

  t.append([x0,y0])


print("Done.  Recall t for table.")


Examples


Results are rounded to five digits.  


Example 1:

dy/dx = 2*x*y + x,  y(0) = 0, h = 0.1, 5 steps

(Real solution:  y = 1/2 * (e^(x^2) - 1))


Results (which matches the exact results):

x = 0.1, y ≈ 0.00503

x = 0.2, y ≈ 0.02041

x = 0.3, y ≈ 0.04709

x = 0.4, y ≈ 0.08676

x = 0.5, y ≈ 0.14201


Example 2:

dy/dx = ln x + y, y(10) = 1

(Real Solution:  y = [∫(ln t * e^(-t) dt, t = 10 to x) + e^(-10)] * e^x


Exact Results:

x = 11, y ≈ 6.74551

x = 12, y ≈ 22.51732

x = 13, y ≈ 65.53659

x = 14, y ≈ 182.60824

x = 15, y ≈ 500.96552


Runge Kutta with h = 1, 5 steps:

x = 11, y ≈ 6.71066

x = 12, y ≈ 22.33376

x = 13, y ≈ 64.78988

x = 14, y ≈ 179.90761

x = 15, y ≈ 491.80768



Runge Kutta with h = 0.1, 50 steps:

x = 11, y ≈ 6.74551   (recall t[10])

x = 12, y ≈ 22.51728   (t[20])

x = 13, y ≈ 65.53643   (t[30])

x = 14, y ≈ 182.60766  (t[40])

x = 15, y ≈ 500.96358  (t[50])


This ends Python week for now, I hope you find this week helpful and resourceful.


Until next time,


Eddie


All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


Thursday, August 4, 2022

Python - Lambda Week: Integration by Simpson's Rule

Python - Lambda Week: Integration by Simpson's Rule



Welcome to Python Week!  This we we're going to cover calculus and the keyword lambda.


Note:  All Python scripts presented this week were created using a TI-NSpire CX II CAS.   As of June 2022, the lambda keyword is available on all calculators (in the United States) that have Python.   If you are not sure, please check your calculator manual. 


Simpson's Rule


The Simpson's Rule estimates numeric integrals by:


∫( f(x) dx, x = a to b) ≈

(b - a) /(3 * n) * (f(a) + 4 * f1 + 2 * f2 + 4 * f3 + .... + 2 * f_n-2 + 4 * f_n-1 + f(b))


n must be an even number of partitions.  The more partitions, the higher the accuracy and the higher computation time.


integrallam.py:  Numeric Integer


from math import *


print("The math module is imported.")

print("Integra of f(x), 6 places")

f=eval("lambda x:"+input("f(x)? "))


# input parameters

a=eval(input("lower = "))

b=eval(input("upper = "))

n=int(input("even parts: "))


# checksafe, add 1 if n is odd

if n/2-int(n/2)==0:

  n=n+1


# integral calculus

s=f(a)+f(b)

w=1

# 1 to n-1

for i in range(1,n):

  w=f(a+i*(b-a)/n)

  s+=(2*w) if (i/2-int(i/2)==0) else (4*w)

s*=(b-a)/(3*n)

print("Integral: "+str(round(s,6)))


All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Wednesday, August 3, 2022

Python - Lambda Week: Derivatives and Newton's Method

Python - Lambda Week: Derivatives and Newton's Method



Welcome to Python Week!  This we we're going to cover calculus and the keyword lambda.


Note:  All Python scripts presented this week were created using a TI-NSpire CX II CAS.   As of June 2022, the lambda keyword is available on all calculators (in the United States) that have Python.   If you are not sure, please check your calculator manual. 


Derivative


The Five Stencil Method is used.  Due to the approximate nature, results are rounded to 5 digits.


f'(x) ≈ (-f(x+2*h) + 8*f(x+h) - 8*f(x-h) + f(x-2*h)) / (12 * h)


h is set to 0.0001 to allow for a wide range of functions and to hopefully prevent float point overflows or underflows.  You can modify h or have the user input a value if you so wish.  


derivlam.py:  Derivative Using the Five Stencil Method


# Math Calculations

#================================

from math import *

#================================


print("The math module is imported.")

f=eval("lambda x:"+input("f(x)? "))


# input x0

x=eval(input("d/dx at x0: "))

h=.0001


# derivative, 5 stencil

d=(-f(x+2*h)+8*f(x+h)-8*f(x-h)+f(x-2*h))/(12*h)

print("round to 5 decimal points")

print("d/dx = "+str(round(d,5)))


Newton's Method


The next script finds the root of f(x) (solve f(x) = 0) with a guess.  


x_n+1 = x_n - f(x_n) / f'(x_n)


The derivative is calculated using the Five Stencil Method.   


I put a limit of 100 iterations because Newton's Method is not always perfect nor this script finds solutions in the complex plane, just the real numbers.  


newtonlam.py


# Math Calculations

#================================

from math import *

#================================

print("The math module is imported.")

print("Solve f(x)=0 to 6 places")

f=eval("lambda x:"+input("f(x)? "))


# input x0

x=eval(input("Guess? "))

h=.0001


w=1

n=1

while fabs(w)>10**(-7):

  d=(-f(x+2*h)+8*f(x+h)-8*f(x-h)+f(x-2*h))/(12*h)

  w=f(x)/d

  x-=w

  n+=1

  if n>100:

    print("iterations exceeded")

    break


if n<101:

  print("x = "+str(round(x,6)))

  print("iterations used: "+str(n))



All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


Tuesday, August 2, 2022

Python - Lambda Week: Plotting Functions

Python - Lambda Week: Plotting Functions


Welcome to Python Week!  This we we're going to cover calculus and the keyword lambda.


Note:  All Python scripts presented this week were created using a TI-NSpire CX II CAS.   As of June 2022, the lambda keyword is available on all calculators (in the United States) that have Python.   If you are not sure, please check your calculator manual. 


Plotting Functions


We can use the line:


f=eval("lambda x:"+input("f(x) = "))


for multiple applications.   Remember, lambda functions are not defined so that they can be used outside of the Python script it belongs to but it lambda functions are super useful!


This code is specific to the Texas Instruments calculators (TI-Nspire CX II (CAS), TI-84 Plus CE Python, TI-83 CE Premium Python Edition, but NOT the TI-82 Advanced Python).    For other calculators, HP Prime, Casio fx-CG 50, Casio fx-9750GIII/9860GIII, Numworks, or computer Python, apply similar language. 


plotlam.py:  Plotting with Lambda


from math import *

import ti_plotlib as plt


# this is for the TI calcs

# other calculators will use their own plot syntax


print("The math module is imported.")

# input defaults to string

# use the plus sign to combine strings

f=eval("lambda x:"+input("f(x) = "))


# set up parameters

x0=eval(input("x min = "))

x1=eval(input("x max = "))


# we want n to be an integer

n=int(input("number of points = "))


# calculate step size

h=(x1-x0)/n


# calculate plot lists

x=[]

y=[]

i=x0

while i<=x1:

  x.append(i)

  y.append(f(i))

  i+=h


# choose color (not for Casio fx-9750/9850GIII)

# colors are defined using tuples

colors=((0,0,0),(255,0,0),(0,128,0),(0,0,255))

print("0: black \n1: red \n2: green \n3: blue")

c=int(input("Enter a color code: "))


# plot f(x)

# auto setup to x and y lists

plt.auto_window(x,y)


# plot axes

plt.color(128,128,128)

plt.axes("axes")


# plot the function

plt.color(colors[c])

plt.plot(x,y,".")

plt.show_plot()



All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


Monday, August 1, 2022

Python - Lambda Week: Building and Asking for Functions

Python - Lambda Week: Building and Asking for Functions


Welcome to Python Week!  This we we're going to cover calculus and the keyword lambda.


Note:  All Python scripts presented this week were created using a TI-NSpire CX II CAS.   As of June 2022, the lambda keyword is available on all calculators (in the United States) that have Python.   If you are not sure, please check your calculator manual. 



Lambda - Introduction


The key word lambda allows us to define a one-line function in Python program for internal use.  Keep in mind, this is different from the define (def-return) structure, where we can define multiline functions and can be used to be imported into other programs or the shell.


I briefly introduced lambda last September:  https://edspi31415.blogspot.com/2021/09/calculator-python-lambda-functions.html



The syntax for lambda is for one argument:


fx=lambda var:define f(var) here


And we can use fx(var) to calculate the lambda function. 




We can use more than one argument, and the syntax looks something like this:


fx=lambda var1, var2, ...:define f(var1, var2, ...)


We use fx(var1,var2,...) to recall and calculate.



Keep in mind, a lambda function can accept many arguments, but can only return one answer.   The script lambdabuild.py shows a short demonstration of the lamdba key word:



lambdabuild.py:   Build a lambda function


from math import *

#================================

# build a lambda function


fx=lambda x:x**2+1

print("x=1, ",str(fx(1)))

print("x=2, ",str(fx(2)))


# lambda can have more than 1 input, but 

# must have only 1 output


gxy=lambda x,y:sqrt(x**2+y**2)

print("x=3, y=4",str(gxy(3,4)))

print("x=6, y=10",str(gxy(6,10)))


Getting User Input


We can ask for a user function by the lines:

fs=input("text here")

fx=eval("lambda var:"+fs)


This can be combined in one line:

fx=eval("lambda var:"+input("prompt"))


For example:

fx=eval("lambda x:"+input("f(x) = "))


The eval function changes a string to an expression to be evaluated.  This is great because we can use eval to change strings to make lambda functions and ask for input of numerical expressions including pi (assuming the math module is imported).


lambda2.py:   Asking for a function


# Math Calculations

#================================

from math import *

#================================

# ask the user to define a function

# input defaults as a string


print("The math module is imported.")

print("Use eval for allow for numeric expressions,")

print("including pi.")

f=eval("lambda x:"+input("f(x) = "))


# ask for three inputs

# use eval to allow for expressions

x1=eval(input("x1? "))

x2=eval(input("x2? "))

x3=eval(input("x3? "))


# calculate

y1=f(x1)

y2=f(x2)

y3=f(x3)


# print results

print("Here are your results:")

print(x1, y1)

print(x2, y2)

print(x3, y3)




All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


Sunday, July 24, 2022

HP Prime: Curve Fitting to Approximate the Zeta Function

HP Prime:  Curve Fitting to Approximate the Zeta Function


Introduction



Here are three approximations for the zeta functions for the positive real numbers x.  For the test data, I used the interval 2 ≤ x ≤ 12.   


For the even integers, exact values are given, otherwise decimal approximations are given.


2,  ζ(2) = π^2 / 6

3,  ζ(3) ≈ 1.202056903

4,  ζ(4) = π^4 / 90

5,  ζ(5) ≈ 1.036927755

6,  ζ(6) = π^6 / 945

7,  ζ(7) ≈ 1.008349277

8,  ζ(8) = π^8 / 9450

9,  ζ(9) ≈ 1.002008392

10,  ζ(10) = π^10 / 93555

11,  ζ(11) ≈ 1.000494189

12,  ζ(12) = 691 * π^12 / 638512875


For x → ∞, ζ → 1


Here are results from three curve fits.  I have tried to include curve fits of at least 10^-2.


Inverse Regression:  Y = A / X + B


Y = 1.42232589936/X+0.81893671619


Average Absolute Error:  5.49240669397ᴇ−2





Logistic Regression:  Y = A / (1 - B * (e^(C * X))


Y = 1.00164385688/(1-2.09727867903*e^(-0.839946048322*X))


Average Absolute Error:  1.41745186091ᴇ−3





Custom Regression:  Y = A + B / X + C X + D X^2


Y = -0.269041227527+(3.20690850188/X)+0.163810293025*X-6.77810226165ᴇ−3*X^2


Average Absolute Error:  1.05418780589ᴇ−2


HP Prime Program:


EXPORT zetamatrix()

BEGIN

LOCAL R,C;

M1:=MAKEMAT(1,11,4);

M2:=MAKEMAT(approx(CAS.Zeta(I+1)),11,1);

FOR R FROM 1 TO 11 DO

M1(R,2):=approx(1/(R+1));

M1(R,3):=approx(R+1);

M1(R,4):=approx((R+1)^2);

END;


END;





Coming up:  Python Week:  August 1 to August 5, 2022

Next Post:  August 2, 2022


Eddie


All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


Saturday, July 23, 2022

HP 32SII Applications: Moments of Inertia, Conductor Temperature Change, Slit Patterns

HP 32SII Applications: Moments of Inertia, Conductor Temperature Change, Slit Patterns


Moment of Inertia - Uniform Disk


The moment of inertia on a uniform disk of radius r is:


I = 2 * π * L * ρ * ∫(r^3 dr, 0, R) 


where ρ = M ÷ ( π * R^2 * L)


The formula of inertia for the uniform disk can be simplified to:


I = M * R^2 * 1/2

where

M = mass of the disk

R = radius of the disk

I = inertia of the center of the mass


HP 32SII Program:


I01  LBL I

I02  INPUT M

I03  INPUT R

I04  x^2

I05  ×

I06  2

I07  ÷

I08  RTN


(12.0 bytes, CK = B55F)


Example:

 

Inputs:

M = 8 kg

R = 0.2 m


Result:

I = 0.16 kg * m^2


Source:

Texas Instruments Incorporated.  Texas Instruments TI-55III Scientific Calculator Sourcebook  Second Edition.  1984



Conductor Temperature Change


The temperature change due to the change of the resistance can be calculated as:


∆t = 1 ÷ α * ( R_2 ÷ R_1 - 1)


where:

∆t = change of temperature in °C

R_2 = new resistance in Ω  (R)

R_1 = new resistance in Ω  (F)

α = temperature coefficient of resistance (A)  (see table below and source)


Selected Temperature Coefficients of Resistance at 20°C (α):


Material:  α


Nickel:  0.005866

Iron:  0.005671

Aluminum:  0.004308

Copper:  0.004041

Silver:  0.003819

Gold:  0.003715

Alloy Steel (99.% iron):  0.003


HP 32SII Program:


T01  LBL T

T02  INPUT A

T03  INPUT R

T04  INPUT F

T05  ÷

T06  1

T07  -

T08  x<>y

T09  1/x

T10  ×

T11 RTN


(16.5 bytes, CK = DDA9)


Example:


Inputs:

A = 0.004041  (α, Copper)

R = 58 Ω  (new resistance)

F = 50 Ω  (old resistance)


Result:

39.594160 °C


Sources:


"Temperature Coefficient of Resistance"  All About Circuits.  Last Retrieved May 17, 2022.  https://www.allaboutcircuits.com/textbook/direct-current/chpt-12/temperature-coefficient-resistance/#:~:text=The%20resistance%2Dchange%20factor%20per,with%20an%20increase%20in%20temperature.


National Radio Institute Alumni Association  Mathematics For Radiotricians Washington, D.C.  1942


Slit Patterns


The intensity of diffraction pattern of the single slit can be calculated by the formula:


I = Im * (sin α ÷ α)^2


where:

Im = potential maximum intensity

α = (π * s * sin θ ÷ λ) in radians

s = slit width

λ = wavelength in Hz

θ = angle of diffraction in degrees


For a double slit:


I = Im * (cos B)^2 * (sin α ÷ α)^2


where:

B is in radians and

B = (π * d * sin θ ÷ λ)

d = distance between slits

θ = angle of diffraction in degrees

α = see the single slit formula above


HP 32SII:

A:  θ

S:  slit wdith

W:  wavelength, λ

I:  maximum intensity


LBL S: single slit

LBL D: double slit, uses LBL S


HP 32SII Programs:


Single Slit:


S01  LBL S

S02  DEG

S03  INPUT A

S04  SIN

S05  INPUT S

S06  ×

S07  π

S08  ×

S09  INPUT W

S10  ÷

S11  RAD

S12  ENTER

S13  SIN

S14  x<>y

S15  ÷

S16  x^2

S17  INPUT I

S18  ×

S19  RTN


(28.5 bytes, CK = 40E0)


Double Slit:


D01  LBL D

D02  XEQ S

D03  DEG

D04  RCL A

D05  SIN

D06  INPUT D

D07  ×

D08  π

D09  ×

D10  RCL÷ W

D11  RAD

D12  COS

D13  x^2

D14  ×

D15  RTN


(22.5 bytes, CK = 8BC7)


Example:


Inputs:

A = 8°

S = 1.96E-6 m

W = 500E-9Hz

I  = 1


Single Slit Calculation:

XEQ S:  0.333496


Double Slit Calculation:

XEQ D

D = 3E-5 m

Result:  0.068409


Source:

Saul, Ken.  The Physics Collection:  Ten HP-41C Programs for First-Year Physics Class  Corvallis, OR.  1986



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Eddie


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